Scalable non-blocking switching network for programmable logic

ABSTRACT

A scalable non-blocking switching network (SN) having switches and intermediate (stages of) conductors that are used to connect a first plurality of conductors to other multiple sets of conductors in a generally unrestricted fashion within respective interconnect resources constraints. The SN can be applied in a wide range of applications, in tandem or hierarchically, to provide a large switch network used in network, routers, and programmable logic circuits. The SN is used to connect a first set of conductors, through the SN, to multiple sets of conductors in a given logic circuit hierarchy whereby the conductors in each of the multiple sets are equivalent or exchangeable, which in term, by construction, makes the first set of conductors equivalent when used in the next level of circuit hierarchy. The SN is scalable for large sized sets of conductors and can be used hierarchically to enable programmable interconnections among large sized circuits.

REFERENCE TO RELATED APPLICATIONS

This is a continuation application of application Ser. No. 12/472,305,filed May 26, 2009 now U.S. Pat. No. 7,768,302, which is a continuationapplication of application Ser. No. 12/174,080, now U.S. Pat. No.7,557,613, filed Jul. 16, 2008, which is a continuation application ofapplication Ser. No. 11/823,257, now U.S. Pat. No. 7,417,457, filed Jun.26, 2007, which is a continuation application of application Ser. No.11/218,419, now U.S. Pat. No. 7,256,614, filed Sep. 1, 2005, which is acontinuation of application Ser. No. 10/814,943, now U.S. Pat. No.6,975,139, filed Mar. 30, 2004, which are hereby incorporated byreference.

TECHNICAL FIELD

Embodiments of this invention relate to switching networks and, inparticular to switching networks used with programmable logic circuits.

BACKGROUND

A programmable logic circuit, also referred to as field programmablegate array (FPGA) is an off the shelf integrated logic circuit which canbe programmed by the user to perform logic functions. Circuit designersdefine the desired logic functions and the circuit is programmed toprocess the signals accordingly. Depending on logic density requirementsand production volumes, programmable logic circuits are superioralternatives in terms of cost and time to market. A typical programmablelogic circuit is composed of logic cells where each of the logic cellscan be programmed to perform logic functions on its input variables.Additionally, interconnect resources are provided throughout theprogrammable logic circuit which can be programmed to conduct signalsfrom outputs of logic cells to inputs of logic cells according to userspecification.

As technology progresses to allow for larger and more sophisticatedprogrammable logic circuits, both the number of logic cells and therequired interconnect resources increases in the circuit. Competing withthe increased number of logic cells and interconnect resources is theneed to keep the circuit size small. One way to minimize the requiredcircuit size is to minimize the interconnect resources while maintaininga certain level of connectivity. Therefore, it can be seen that as thefunctionality implemented on the chip increases, the interconnectionresources required to connect a large number of signals can be quicklyexhausted. The trade-offs are either to provide for a lower utilizationof logic cells in a circuit while keeping the circuit size small or toprovide more routing resources that can increase the circuit sizedramatically.

There has been a progression of increasingly complex connection stylesover the last forty years in the field of programmable logic circuits.L. M. Spandorfer in 1965 describes possible implementation of aprogrammable logic circuit using neighborhood interconnection, andconnections through multiple conductors using switches in a Closnetwork. R. G. Shoup in his PhD thesis of 1970 describes both the use ofa neighborhood interconnect and the use of a bus for longer distanceinterconnect.

Freeman in the U.S. Pat. No. 4,870,302 of 1989 describes a commercialimplementation of a FPGA using neighborhood interconnects, short (lengthone, called single) distance interconnects, and global lines for signalssuch as clocks. The short distance interconnects interact with theinputs and outputs of logic cells where each input is connected throughswitches to every short wire neighboring to a logic cell and horizontaland vertical short wires connect through a switch box in a junction. ElGamal et al. in U.S. Pat. No. 4,758,745 introduces segmented routingwhere inputs and outputs of logic cells interact with routing segmentsof different lengths in one dimension.

Peterson et al. in U.S. Pat. No. 5,260,610 and Cliff et al. in U.S. Pat.No. 5,260,611 introduce a local set of conductors interfacing with a setof logic elements where every input of the logic elements is connected,through switches, to every local conductor in the set; additional chiplength conductors are introduced both horizontally and vertically wherethe horizontal conductor can connect to the vertical conductors and thehorizontal conductors connect to multiple local conductors. In U.S. Pat.No. 4,870,302, U.S. Pat. No. 4,758,745, U.S. Pat. No. 5,260,610, andU.S. Pat. No. 5,260,611, the input conductor of a logic cell has fullconnections to the set of local conductors (e.g. for n-inputs andk-local conductors, there is n×k switches connecting the inputs to thelocal conductors. A multiplexer (MUX) scheme may also be used so thatthe number of transistors is reduced.). In U.S. Pat. No. 4,870,302, U.S.Pat. No. 4,758,745, U.S. Pat. No. 5,260,610, and U.S. Pat. No.5,260,611, the general interconnect resources are limited to one or twodifferent lengths (i.e. singles of U.S. Pat. No. 4,870,302, local andchip length in U.S. Pat. No. 5,260,610 and U.S. Pat. No. 5,260,611) orlimited in one dimension (i.e. different lengths horizontally in U.S.Pat. No. 4,758,745, local vertically in U.S. Pat. No. 5,260,610 and U.S.Pat. No. 5,260,611).

Camarota et al. in U.S. Pat. No. 5,144,166 and Kean in U.S. Pat. No.5,469,003 introduce a routing scheme with more than two differentlengths in both dimensions with limitations in the reach of thoseconductors. While U.S. Pat. No. 5,144,166 allows each wire to beselectively driven by more than one possible driving source, U.S. Pat.No. 5,469,003 is limited to be unidirectional in that each wire ishardwired to a MUX output. The connectivity provided in both U.S. Pat.No. 5,144,166 and U.S. Pat. No. 5,469,003 are very low, based on thepremises that either connections are neighborhood or relatively local,or logic cells itself can be used as interconnection resources insteadof performing logic functions. Ting in U.S. Pat. No. 5,457,410, U.S.Pat. No. 6,507,217, U.S. Pat. No. 6,051,991, U.S. Pat. No. 6,597,196describe a multiple level architecture where multiple lengths ofconductors interconnect through switches in a hierarchy of logic cells.

Young et al. in U.S. 2001/0007428 and U.S. Pat. No. 5,914,616 describean architecture with multiple lengths of wires in two dimensions (threein each dimension) where for short local connections, a near cross-barscheme is used where a set of logic cells outputs are multiplexed to areduced set of output ports which then interface to other interconnectresources. The longer wires generally fan-in into shorter length wiresin a respective dimension. Reddy et al. in U.S. Pat. No. 6,417,694discloses another architecture where inter-super-region, inter-region,and local conductors are used. A cross-bar scheme is used at the lowestlevel (using MUXs) for the local wires to have universal access to theinputs of the logic elements. Reddy et al. in U.S. Pat. No. 5,883,526discloses various schemes having circuit reduction techniques in thelocal cross-bar.

At the base level of circuit hierarchy, four-input Look Up Table (LUT)logic cells are commonly used. There are two advantages in using a LUTas the base logic cell. One advantage is that the circuit allows anyfour-input, one output Boolean functions with programmable controls.Another advantage is that the four inputs are exchangeable and logicallyequivalent. Hence it does not matter which signal connecting to whichinput pin of the LUT for the LUT to function correctly as long as thosefour signals connect to the four inputs of the LUT.

A common problem to be solved in any programmable logic circuit is thatof interconnectivity, namely, how to connect a first set of conductorscarrying signals to multiple sets of conductors to receive those signalswhere the logic cells originating the signals and the logic cellsreceiving the signals are spread over a wide area in an integratedcircuit (i.e., M outputs of M logic cells where each output connects toinputs of multiple number of logic cells). A highly desirable but inmost cases impractical solution is to use a cross bar switch where everyconductor of the first set is connectable to every conductor in themultiple sets of conductors directly through a switch. Prior solutionsin one degree or another try to divide the connectivity problem intomultiple pieces using a divide and conquer strategy where local clustersof logic cells are interconnected and extended to other clusters oflogic, either through extensions of local connections or using longerdistance connections. These prior interconnect schemes are ad hoc andmostly based on empirical experiences. A desired routing model orinterconnect architecture should guarantee full connectability for alarge number of inputs and outputs (through programmable interconnectconductors) connecting to multiple sets of conductors over a large partof the circuit all the time.

Complicated software is necessary to track interconnect resources whilealgorithms are used to improve interconnectability during the place androute stage implementing a custom design using the programmable logiccircuit. Thus, it is desirable to have a new interconnect scheme forprogrammable logic circuits where the routability or interconnectabilitymay be guaranteed in a more global scale while the cost ofinterconnections remains low in terms of required switches and thesoftware efforts in determining a place and route for custom designimplementation are simplified.

BRIEF DESCRIPTION OF THE DRAWINGS

The objectives, features, and advantages of the present invention willbe apparent from the following detailed description in which:

FIG. 1 illustrates an embodiment of a circuit with four four-input logiccells and two flip flops using a scalable non-blocking switching network(SN).

FIG. 2 illustrates one embodiment of a circuit using a stage-0 scalablenon-blocking switching network (0-SN) with eleven M conductors accessingfour sets of four N conductors.

FIG. 3 illustrates one embodiment of a circuit using two stage-0scalable non-blocking switching networks with each 0-SN having five Mconductors accessing four sets of two N conductors.

FIG. 4 illustrates one embodiment of a circuit using a stage-1 scalablenon-blocking switching network (1-SN) with eleven M conductors accessingfour sets of four N conductors through N sets of four intermediateconductors.

FIG. 5 illustrates one embodiment of a circuit using a stage-1 scalablenon-blocking switching network with twelve M conductors accessing foursets of four N conductors through fewer intermediate conductors.

FIG. 6 illustrates one embodiment of a circuit using a stage-1 scalablenon-blocking switching network with twelve M conductors accessing foursets of four N conductors with stronger connectivity property.

FIG. 7 illustrates one embodiment of a reduced stage-1 scalablenon-blocking switching network with fewer switches.

FIG. 8 illustrates one embodiment of a larger size stage-1 scalablenon-blocking switching network.

FIG. 9 illustrates one embodiment of a stage-1 scalable non-blockingswitching network with sixteen M conductors.

FIG. 10 is a block diagram illustrating one embodiment of a stage-2scalable non-blocking switching network (2-SN) and a circuit with fourlogic circuits of FIG. 1, each using the scalable non-blocking switchingnetwork of FIG. 9.

FIG. 11A illustrates a block diagram embodiment of the stage-2 scalablenon-blocking switching network of FIG. 10.

FIG. 11B illustrates one embodiment of the first part of the stage-2scalable non-blocking switching network of FIG. 11A.

FIG. 12 illustrates one embodiment of a stage-1 scalable non-blockingswitching network implementing the second part of the 2-SN of FIG. 11A.

DETAILED DESCRIPTION

An innovative scalable non-blocking switching network (SN) which usesswitches and includes intermediate stage(s) of conductors connecting afirst plurality of conductors to multiple sets of conductors where eachconductor of the first plurality of conductors is capable of connectingto one conductor from each of the multiple sets of conductors throughthe SN, is first described. The scalable non-blocking switching networkcan be applied in a wide range of applications, when used, either in asingle stage, or used hierarchically in multiple stages, to provide alarge switch network used in switching, routers, and programmable logiccircuits. A scalable non-blocking switching network is used to connect afirst set of conductors, through the SN, to multiple sets of conductorswhereby the conductors in each of the multiple sets are equivalent orexchangeable, for example, the conductors of one of the multiple setsare the inputs of a logic cell (which can be the inputs of a LUT orinputs to a hierarchy of logic cells). The scalable non-blockingswitching network in this present invention allows any subset of a firstset of conductors to connect, through the SN, to conductors of a secondmultiple sets of conductors, so that each conductor of the subset canconnect to one conductor from each set of the multiple sets ofconductors.

In the following description, for purposes of explanation, numerousspecific details are set forth in order to provide a thoroughunderstanding of the present invention. It will be apparent to oneskilled in the art that embodiments of the present invention may bepracticed without these specific details. In other instances, well-knownstructures and circuits are shown in block diagram form in order toavoid unnecessarily obscuring the present invention. For purpose ofdescription, unless otherwise specified, the terms program controlledswitch and switch are interchangeable in the context of thisdescription: the terms program configured logic cell, logic cell, cell,Look Up Table (LUT), programmable logic cell are interchangeable in thecontext of this description; the terms conductor, signal, pin, port,line are interchangeable in the context of this description. It shouldalso be noted that the present invention describes embodiments which useprogram control means to set the states of switches utilized, thiscontrol means can be one time, such as fuse/anti-fuse technologies, orre-programmable, such as SRAM (which is volatile), FLASH (which isnon-volatile), Ferro-electric (which is non-volatile), etc. Hence thepresent invention pertains to a variety of processes, including, but notlimited to, static random access memory (SRAM), dynamic random accessmemory (DRAM), fuse/anti-fuse, erasable programmable read-only memory(EPROM), electrically erasable programmable read-only memory (EEPROM)such as FLASH, and Ferro-electric processes.

The concept of scalable non-blocking switching networks utilized in aprogrammable logic circuit described herein can be generally applied toallow unrestricted connections between a plurality of conductors tomultiple sets of conductors, as long as the connection requirements donot exceed the available conductors.

When a program controlled switch is used to interconnect one conductorto another conductor, a driver circuit may be coupled to the switch toimprove the speed of the signal traversing those conductors.Additionally, if multiple conductors (signals) fan-in to a conductorthrough program controlled switches, it is possible to use a MUX scheme,if desired, to either reduce loading on the conductor or to reducecircuit size, or both, depending on the process technology used. In thecase where a MUX is used, the multiple switches are converted into a newswitch mechanism where, the number of effective states are the same asthe number of switches, connectivity is enabled by choosing theparticular state (corresponding to the switch if multiple switches wereused) in connecting two conductors and the states are determined byprogrammable control.

Various types of scalable non-blocking switching networks are describedincluding, but not limited to: stage-0 scalable non-blocking switchingnetwork (0-SN), stage-1 scalable non-blocking switching network (1-SN),stage-2 scalable non-blocking switching network (2-SN) and extensions tomulti-stage scalable non-blocking switching networks and the use ofthose scalable non-blocking switching networks hierarchically inproviding interconnectivity to programmable logic circuits.

FIG. 1 shows an embodiment of a cluster (CLST4) circuit 100 including ascalable non-blocking switching network 200 and including k number offour-input logic cells (where k=4 in this embodiment) 10, 20, 30 and 40and two Flip-Flops 50 and 60. Each of the logic cells 10-40 has fourinputs 101-104 (N0[0-3]) for cell 10, four inputs 105-108 (N1[0-3]) forcell 20, four inputs 109-112 (N2[0-3]) for cell 30 and four inputs113-116 (N3[0-3]) for cell 40, with four conductors 121-124 as the fouroutputs for cells 10-40 respectively. Switches 151-156 and 159, 160 areused to control whether a logic cell output drives a Flip-Flop or thelogic cell outputs to circuit 100 outputs 125-128 directly. TheFlip-Flops 50, 60 output to circuit 100 outputs 125-128 using switches157, 158, 161 and 162. Additionally, conductor 131 can drive conductor101 of cell 10 through switch 141 and conductor 105 of cell 20 throughswitch 142. Similarly, conductor 132 can drive cells 30 and 40 throughswitches 143 and 144, respectively. Cell 20 can drive a neighboringCLST4 circuit (not shown in FIG. 1) through output 122 using switches145 to conductor 133. Output 124 of cell 40 drives out to conductor 134through switch 146 in FIG. 1. Three other signals 135-137 are used tocontrol the Flip-Flops as SET, CLOCK, and CLEAR, respectively.Additionally, FIG. 1 has (X+1) conductors 180 (M[0-X]) fanning in todrive the sixteen inputs 101-116 using a switch network MTX 200. Theconductors M[0-X] 180 are called M conductors where M is equal to thenumber of conductors (X+1) in the embodiment of FIG. 1. The inputconductors Ni[0-3] for i=[0-(k−1)] 101-116 are called the Ni conductorswhere Ni is equal to the number of inputs which is four in theembodiment of FIG. 1. For purpose of illustration, the size Ni=N=4 isshown in FIG. 1. Alternatively, each Ni can have a different sizewithout changing the connectivity property described herein.

FIG. 2 shows an embodiment where MTX 200 of FIG. 1 is represented by astage-0 scalable non-blocking switching network (0-SN) 300; each Nconductor 101-116 is connectable to (M−N+1) conductors of the Mconductors (e.g., conductors 180 of FIG. 1) 201-211 (M[0-10]), thenumber of switches shown in FIG. 2 for each input conductor ofconductors 101-116 is thus (M−N+1)=8 for the 0-SN 300 of FIG. 2. Theswitch network 0-SN 300 allows any subset of M conductors 201-211 todrive one input conductor of each of the logic cells 10-40 using theswitches of 300 without any blocking as long as the number ofconnections do not exceed the available interconnect resources (i.e.,the number of M conductors driving the inputs of any of the logic cellscan not exceed the number of inputs of the logic cell). The scheme ofFIG. 2 is an improvement over a cross bar connection where instead of afull switch matrix comprising M×(k×N)=11×(4×4)=176 switches, the numberof switches is (M−N+1)×(k×N)=128. The 0-SN 300 in FIG. 2 allows theabove stated connectivity by assuming the four inputs for each of thelogic cells as exchangeable or logically equivalent (i.e., conductors101-104 of cell 10 of FIG. 1 are equivalent or exchangeable) so it isonly necessary to connect a particular M conductor (i.e. M[4] conductor205) to any input pin of a given logic cell (i.e., conductor 101 out ofconductors 101-104 of cell 10 of FIG. 1 using switch 222) if theconnection requirement is to connect the particular M conductor to thegiven logic cell.

Depending on technology used in the programmable circuits, some areaminimization can be accomplished. For example, using a SRAM memory cellwith six transistors as the program control for each switch implementedusing a passgate, the eight switches 221-228 of FIG. 2 per input line101 will require fifty six transistors. Instead, an eight input MUXusing three memory bits can be used to control eight states toeffectively replace the eight SRAM bits and eight switches. In the MUXscheme, three bits, fourteen passgates and perhaps one inverter (toregenerate the signal) uses thirty four transistors which is a largereduction from the fifty six transistors used with eight SRAM memorycells as the program control for each switch. The loading on conductor101 will be reduced using the MUX implementation while there areadditional delays due to the eight to one MUX.

FIG. 3 shows an embodiment where MTX 200 of FIG. 1 is represented byusing two stage-0 scalable non-blocking switching networks 330 and 320with M=Ma+Mb=10 conductors 301-310 composed of subgroups Ma=[A0-A4]=5301-305 conductors and Mb=[B0-B4]=5 306-310 conductors. Each Nb=2 forthe upper two input conductors of each of the four logic cells (composedof conductors 101-102 for cell 10, conductors 105-106 for cell 20,conductors 109-110 for cell 30 and conductors 113-114 for cell 40) andNa=2 for the lower two input conductors for each of the k=four logiccells (composed of conductors 103-104 for cell 10, conductors 107-108for cell 20, conductors 111-112 for cell 30 and conductors 115-116 forcell 40). A full sized stage-0 scalable non-blocking switching networkof FIG. 3 would have (M−N+1)=10−4+1=7 program controlled switches perinput conductor. Instead, in the embodiment of FIG. 3, the number ofinput switches is only four because of the separate Ma conductors and Mbconductors (with Ma=Mb=5) and the number N is broken into two parts(with Na=Nb=2). As such, the number of program controlled switches perinput conductor in network 330 is Ma−Na+1=5−2+1=4 and the use of programcontrolled switches per input conductor in network 320 is Mb−Nb−1=4.While it is true that the Ma 301-305 conductors connecting to the lowertwo inputs of the four logic cells using network 330 maintain theconnectivity illustrated in FIG. 2 (and similar for Mb conductors306-310 to the lower two inputs of the four logic cells using network320), it is not true that any arbitrary use of [A0-A4], [B0-B4] tofan-in to the four logic cells is so. This constraint prevents arbitraryassignments of M conductors connecting to the N conductors through thetwo O-SNs 320 and 330 of FIG. 3. However, the stage-0 scalablenon-blocking switching networks 320 and 330 together can be an economicimplementation to provide good connectivity for a programmable logiccircuit while the software efforts in book-keeping and tracking theallowable M conductors usage are more complex than the scheme of FIG. 2.FIG. 3 allows at least eight M conductors out of ten to be arbitrarilyconnected to the inputs of the four logic cells, where each oneconductor connecting to one input to each of the four logic cells usingnetworks 320 and 330; the constraint here is that the ten conductors cannot be arbitrarily assigned as in the FIG. 2 case.

In embodiments of the present invention, a first group of conductors isconnected to multiple groups of equivalent conductors using a switchnetwork. Thus far a 0-SN has been presented, where there are (M−N+1)×N×kswitches to provide unrestricted connections between a first set of Mconductors to multiple k sets of N conductors where any subset of Mconductors can connect to one conductor to each of the k sets of Nconductors using the 0-SN without any blockage.

FIG. 4 illustrates an alternative embodiment scheme where the number ofswitches used in the switch network can be greatly reduced withoutchanging the connectivity property of the 0-SN. FIG. 4 shows anembodiment where MTX 200 of FIG. 1 is represented by using a stage-1scalable non-blocking switching network (1-SN). The 1-SN 400 connects aM conductor of conductors 401-411 to a N conductor of conductors 101-116using two switches of the 1-SN 400 plus one intermediate conductor.Instead of directly connecting the M conductors 201-211 to the k sets ofN conductors 101-116 through the network 300 of FIG. 2 where 128switches are used, the 1-SN 400 in FIG. 4 connects a M conductor 407(M[6]) to a N conductor 109 by first connecting to an intermediate Iconductor 454 through switch 437 and then to the N conductor 109 throughswitch 441 of sub-network 450. Similarly, the same M conductor 407 canconnect to N conductors 101, 105, and 113 through the same intermediateconductor 454 through switches 442, 443 and 444, respectively. The 1-SN400 of FIG. 4 has ninety six switches which is a 25% reduction in thenumber of switches compared with the 0-SN 300 of FIG. 2. It is possibleto reduce the number of switches required in a 0-SN by creating ascalable non-blocking switching network with intermediate stage(s) ofinterconnect where each of the M conductors can connect, arbitrarily, toa conductor from each of k sets of N conductors. The scalablenon-blocking switching network is capable of connecting a M conductor tomore than one conductor from each of k sets of N conductors; however,logically it is not necessary to connect to more than one conductor ineach of the N conductors.

FIG. 4 illustrates a 1-SN 400 with N sets of intermediate conductorsI_(i) for i=[1-N], where there are eleven M conductors 401-411, foursets of N conductors, 101-104, 105-108, 109-112 and 113-116, and k isfour. The first intermediate conductors I₁, for example, are the fourconductors 451-454 that associate with the first input for each of the Nconductors, thus conductors 101, 105, 109 and 113. Similarly, conductors461-464 are the I₄ conductors associated with conductors 104, 108, 112,and 116. The (M−N+1) switches for each conductor of the N conductors ina 0-SN are distributed amongst the corresponding I_(i) conductors inFIG. 4. For example, the eight switches 431-438 coupling the Mconductors 401-408 are distributed to the I₁ conductors 451-454 whereeach of the I₁ conductors couples to [(M−N+1)/I₁] switches, which istwo. In the example of FIG. 4, the number of intermediate conductors ineach of the I_(i) conductors is four. Generally, different I_(i) neednot be a uniform number (as described below). The 1-SN 400 of FIG. 4 has[(M−N+1)×N+sum_(i=[1-N])(I_(i)×k)]=32+64=96 switches where I_(i) is thenumber of intermediate conductors in each of N sets of I_(i)intermediate conductors. The 1-SN 400 of FIG. 4 allows the sameconnectivity property as the respective 0-SN 300 of FIG. 2, connectingany conductor of the M conductors to one conductor of each k sets of Nconductors through two switches and one intermediate conductor in 1-SN400.

In the 1-SN 400 of FIG. 4, any N-tuple of M conductors have theappropriate choice of switches to different N sets of I_(i) conductors.For example, conductors 401, 404, 405, and 410 are the four-tuple (N=4)of M conductors where conductor 401 connects to conductor 451 (of the I₁conductors) through switch 431; conductor 404 connects to conductor 466(of the I₂ conductors) through switch 446; conductor 405 connects toconductor 467 (of the I₃ conductors) through switch 447; and conductor410 connects to conductor 464 (of the I₄ conductors) through switch 427.Any subset of the N-tuple of M conductors has the same propertyconnecting to the intermediate conductors. Additionally, eachintermediate conductor of I_(i) conductors is connectable to one Nconductor in each of the k sets of N conductors. For example, anyconductor of conductors 451-454 is connectable, through the switches insub-network 450, to conductors 101, 105, 109 and 113. Similarly, anyconductor of conductors 461-464 is connectable to conductors 104, 108,112 and 116 through switches in sub-network 420.

FIG. 5 illustrates an alternative embodiment of a 1-SN representing theMTX 200 of FIG. 1. In 1-SN 500 there are twelve M conductors 501-512,four sets of N conductors 101-116, and N sets of intermediate I₁conductors 521-523, I₂ conductors 524-526, I₃ conductors 527-529, and I₄conductors 530-532 where M=I₁+I₂+I₃+I₄ or I_(i)=M/N=3. The number ofswitches in FIG. 5 is [(M−N+1)×N+sum_(i=[1-N])](I_(i)×k)=36+48=84. Acorresponding 0-SN would have one hundred and forty four switches and across bar would have one hundred and ninety two switches. Theconnectivity property of the 1-SN 500 of FIG. 5 is the same as thosediscussed earlier with respect to 1-SN 400 of FIG. 4 with fewerintermediate conductors and switches. The illustrations in FIG. 4 andFIG. 5 have the first set of intermediate I₁ conductors (conductors451-454 of FIG. 4 and conductors 521-523 of FIG. 5) connecting toconductors 101, 105, 109, 113, which are the first input of each of thefour logic cells 10-40 of FIG. 1, through switches of sub-network 450 ofFIG. 4 and switches of sub-network of 540 of FIG. 5, respectively. Anequally effective alternative is to connect each set of I_(i) conductorsto any one conductor (instead of the i^(th) one) from each of the fourlogic cells as long as each of the four inputs of a particular logiccell in this example are covered by a different set of conductors.

FIG. 6 illustrates an embodiment of a different version of a stage-1scalable non-blocking switching network having a stronger connectivityproperty than the 1-SN 500 of FIG. 5. While requiring more switches, thetwelve M conductors, 601-612 (M[0]-M[11]) of 1-SN 600 are connectable toall the conductors in each of the N sets of intermediate conductors621-623, 624-626, 627-629, 630-632. This is in contrast to the couplingto (M−N+1) conductors of the M conductors in FIG. 4 and FIG. 5. In 1-SN600, conductors 601-612 are connectable to I₁ conductors 621-623 throughthe switches in sub-network 620. Conductors 601-612 are connectable toI₂ conductors 624-626 through the switches in sub-network 640.Conductors 601-612 are connectable to I₃ conductors 627-629 through theswitches in sub-network 650. Conductors 601-612 are connectable to I₄conductors 630-632 through the switches in sub-network 660. The twelve Mconductors 601-612 in FIG. 6 have a stronger connectivity propertycompared to the 1-SN 500 of FIG. 5 where one conductor of M/I_(i)conductors can be program selected to connect to a specific N conductorsof any of the k sets. As an example, in the embodiment of FIG. 6, any ofN-tuples conductors 601-604, 605-608, 609-612 (of M conductors) canconnect to any specific input conductor of any of the four (k=4) sets ofN conductors using the 1-SN, but the conductors within each four-tuplesare mutually exclusive to the specific input conductor. The number ofswitches required in this 1-SN 600 of FIG. 6 is[M×N+sum_(i=[1-N])(I_(i)×k)]=48+48=96 switches.

The difference between a 0-SN and a 1-SN in terms of switches requiredis the difference between [(M−N+1)×N×k] and [(M−N+1)×N+sum (I_(i)×k)] inthe case of FIG. 5 where (M−N+1) of the M conductors are connectablethrough the 1-SN to the I_(i) conductors in each of the N sets of I_(i)conductors. The difference between a 0-SN and a 1-SN in terms ofswitches required is the difference between [M×N×k] and[M×N+sum_(i=[1-N])(I_(i)×k)] in the case of FIG. 6. If we simplify eachI_(i)=k, then M is at least [k+N+1/(k−1)] for the case of FIG. 5 and Mis at least [k+1+1/(k−1)], it is worthwhile to note that the scheme ofFIG. 5 still works for M to be less than the number(s) above.Additionally, in order for the scheme of a 1-SN to work, the number ofswitches per intermediate conductor [(M−N+1)/I_(i)] may not be greaterthan N without loosing the non-blocking characteristics of the SN. Thenumber, [(M−N+1)/I_(i)], may not be an integer, in the case, an integernumber P_(i) is used by rounding the number (M−N+1)/I_(i) up or downwhile the sum_(i=[1-N])P_(i)=(M−N+1). Similarly, for the case of FIG. 6,M is used instead of (M−N+1) so P_(i) would be the integer rounding upor down (MAO, while the sum_(i=[1-N])P_(i)=M. Furthermore, in theexamples of FIG. 4 and FIG. 5, the number of intermediate conductorssum_(i=[1-N])I_(i) is bounded to be at least M and if k×N is greaterthan M, the sum_(i=[1-N])I_(i) can either be M or k×N or some number inbetween; while each individual I_(i) is bounded by M/N, k or some numberin between and since M/N may not be integer divisible, I_(i) is aninteger by rounding up or down M/N, hence we can see that individualI_(i) may not be uniform among all i for i=[1-N].

FIG. 7 illustrates an embodiment where the number of switches in theembodiment of FIG. 6 is reduced without much change to the connectivityproperty of the 1-SN. FIG. 7 represents the reduction where conductor601 is shorted to conductor 621, conductor 602 is shorted to conductor624, conductor 603 is shorted to conductor 627, and conductor 604 isshorted to conductor 630 in FIG. 6; where the sixteen switches insub-network 670 of FIG. 6 are deleted and the number of switches iseighty in FIG. 7 instead of ninety six in FIG. 6. The 1-SN 700 minussub-networks 710, 720, 730 and 740 in FIG. 7 with M conductors 605-612,has the same stronger connectivity property of the 1-SN 600 described inFIG. 6 and is a 1-SN with M=8. It is possible to further reduce thenumber of switches, for example, by shorting more M conductors to theintermediate conductors, but the connectivity property would be muchreduced and the software efforts in determining a connection patternwould become increasingly more complex.

FIG. 8 illustrates an embodiment of a 1-SN with M=48, k=4, N=16 andI_(i)=3 for i=[1-16]. Because there are 720 switches in 1-SN 800, a 0-SNwould require 2112 switches and a cross bar would require 3072 switches.Each of the N(=16) sets of I_(i) intermediate conductors, for example,I₁₆, has three conductors (inside sub-network 810) where the I₁₆conductors couple to (M−N+1)=33 M conductors in FIG. 8, each of theintermediate conductors couples to eleven M conductors through theeleven switches in sub-network 811. By introducing an intermediateconductor and an extra switch in the connection path, the 1-SN 800provides a large reduction in number of switches required compared tothat of a 0-SN.

In the various embodiments examples have been used where M is less thank×N and M conductors are the conductors carrying fan-in signals whilethe k sets of N conductors are the conductors to receive those fan-insignals. This need not be the case. We can simply have a SN where M islarger than k×N. Alternatively, we can consider, for example, theconductors 101-104, 105-108, 109-112 and 113-116 in FIG. 6 as sixteenoutputs from four clusters of logic cells and using the 1-SN for thepurpose of output reduction from sixteen to twelve where any subset oftwelve outputs out of sixteen outputs can be selected using the 1-SN.Additionally, the conductors 101-104, 105-108, 109-112 and 113-116 inthe various figures need not be either inputs or outputs of logic cellsbut may be a plurality of equivalent conductors where connection to anyof the conductor in one plurality of equivalent conductors is sufficientas opposed to connection to a particular conductor in the plurality ofequivalent conductors.

In designing interconnection architecture for programmable logiccircuits, it may be important to provide reasonable connectivity andadequate interconnection resources based on engineering trade-offs sucha circuit size, speed and ease of software to place and route a customerspecified design. There is a ratio R between the M conductors and the ksets of N conductors where R=M/(k×N); if R is too small, theconnectivity is more limited than a larger R. The circuit in FIG. 6, forexample, has R=0.75. We shall call R the expansion exponent in buildingup the hierarchy of circuits using scalable non-blocking switchingnetworks. A commonly used expansion exponent, for the design of aprogrammable logic circuits using the scalable non-blocking switchingnetworks, is in the range between 0.5 and 1.0 and the choice isdependent on factors such as engineering design trade-offs (i.e., logicutilization, circuit area minimization, ease of software place androute, etc.), technology used (i.e., SRAM, anti-fuse, etc.), etc. It issometimes advantageous to exceed the range in parts of the circuits, forexample, in an output reduction where a large number of outputs arereduced to a lesser number using a SN.

The previous discussion dealt with using 0-SN and 1-SN which can be usedto build up a circuit hierarchy for the interconnect of programmablelogic cells whereby each level of hierarchy contains severalprogrammable logic circuits with associated 0-SN and/or 1-SN to connectto various conductors throughout the circuits using the various scalablenon-blocking switching networks. The previously described schemes allowconnection to an arbitrary signal at any level of circuit hierarchy toreach an input of any of the logic cells within the hierarchy using the0-SNs and the 1-SNs as long as interconnect resources and logiccapacities remain available.

Below is described a scheme in building up a programmable logic circuitusing stage-1 and stage-2 scalable non-blocking switching networkshierarchically. FIG. 9 illustrates an embodiment of the MTX circuit 200in the CLST4 circuit 100 in FIG. 1 using a stage-1 scalable non-blockingswitching network with sixteen M conductors 901-916, four sets of Nconductors 101-104, 105-108, 109-112, 113-116 where N=4, and N sets ofI_(i) conductors 931-934, 935-938, 939-942, 943-946, for i=[1-N] whereeach I_(j)=M/N=4; the expansion exponent R is 1.0 in the embodiment ofFIG. 9.

By construction in building a programmable circuit, for example, using a1-SN 900 of FIG. 9, any subset of the M conductors 901-916 can beindividually connected through the 1-SN 900 to one conductor in each ofthe k sets of N conductors. Those M conductors themselves then becomelogically equivalent. For any signal originating somewhere outside theCLST4 circuit 100 of FIG. 1 to connect up to four inputs from each ofthe four logic cells 10-40 (one from conductors 101-104, one fromconductors 105-108, one from conductors 109-112, and one from conductors113-116) of FIG. 1; it is only necessary to connect to one of the Mconductors. Thus, those M conductors 901-916 can be treatedhierarchically as the N conductors (where N=16) where multiple new ksets of those new N conductors each having a circuit including fourlogic cells and two Flip Flops together with the 1-SN are to beselectively connected through a new switch network such as a SN by a newset of M conductors. This process can be repeated till a desired circuitsize is reached while the desired circuit allows unrestrictedconnectivity as discussed above.

FIG. 10 illustrates a block diagram embodiment of a next level ofcircuit hierarchy CLST16 1000 using four sets of CLST4 100 of FIG. 1(CLST4 1010, CLST4 1020, CLST4 1030, CLST4 1040 of FIG. 10) wherecircuit MTX 200 is implemented using the 1-SN 900 of FIG. 9 and astage-2 scalable non-blocking switching network of circuit MTX16 1050with sixty four M conductors having forty eight conductors 1055(M[0-47]) and sixteen conductors 1056 (OW[0-7], OE[0-7]) and four setsof N conductors 1060, 1070, 1080, 1090 where each of the N conductorshas sixteen conductors which correspond to the sixteen M conductors901-916 of FIG. 9. In FIG. 10, sixteen conductors 1056 of the sixty fourM conductors 1055 and 1056 directly connect to the four outputs 1065,1075, 1085, 1095 of the four CLST4 100 circuits 1010, 1020, 1030, 1040.The sixteen conductors 1056 (OW[0-7], OE[0-7]) having four sets of fourconductors and each of the four conductors corresponds to the fouroutputs 125-128 (0[0-3]) of the CLST4 100 circuit of FIG. 1. Theexpansion exponent R is again 1.0 in this circuit 1000.

The use of scalable non-blocking switching networks in this next levelof circuit hierarchy, connecting large number of conductors to multiplesets of conductors, is illustrated in FIG. 11A. FIG. 11A illustrates anembodiment, in block diagram form, of circuit MTX16 1050 of FIG. 10where the sixty four M conductors 1101 (M[0-47], OW[0-7], OE[0-7])correspond to conductors 1055 and 1056 of FIG. 10. The first stage ofintermediate conductors is composed of N0 (where N0=4) sets of sixteenI0_(i) conductors (where I0_(i)=M/N0=16 for i=[1-N0]) 1150, 1160, 1170,and 1180. The M conductors 1101 interface to the first four sets ofintermediate stage I0_(i) conductors 1150, 1160, 1170, 1180 using theswitches of sub-networks 1110, 1120, 1130 and 1140. FIG. 11B illustratesa scheme where conductors 1101 connects to conductors 1160 throughsub-network 1120. The connection scheme where conductors 1101 connect toconductors 1150 through sub-network 1110, and to conductors 1170 throughsub-network 1130, and to conductors 1180 through sub-network 1140 arethe same as sub-network 1120 of FIG. 11B. The number of switches usedbetween the M conductors 1101 to the four sets of first stageintermediate conductors 1150, 1160, 1170, 1180 in this embodiment isM×N0=256. As described in relation to FIG. 5, an alternativeimplementation is to have (M−N0+1)×N0 switches instead.

FIG. 12 illustrates an embodiment of circuit TA1 1165 where conductors1160 is the second N0 set of I0_(i) conductors, where i=2 and I0_(i)=16;intermediate conductors 1201-1216 (which correspond to conductors 1160of FIG. 11A) interface to sixteen conductors 1241-1256 (which correspondto conductors 1161-1164 of FIG. 11A). Sub-networks 1155, 1175, 1185 ofFIG. 11A are the same circuit as sub-network 1165 to interconnectconductors 1150, 1170, 1180 to conductors 1151-1154, 1171-1174,1181-1184 of FIG. 11A, respectively.

In FIG. 12, the circuit TA1 is a 1-SN 1165 of FIG. 11A where Mconductors 1201-1216 are the sixteen intermediate I0₂ conductors 1160(I1_(—)1[0-15]) of FIG. 11A; sixteen intermediate conductors 1221-1236are composed of N1 (=4) sets of I1_(2j) (I1_(2j)=M/N1=4) conductors fori=2, j=[1-N1]: conductors 1221-1224, 1225-1228, 1229-1232, 1233-1236.The I1_(2j) conductors connects to the four sets of destinationconductors 1241-1244, 1245-1248, 1249-1252, 1253-1256 for j=[1-N1],respectively. The 1-SN 1165 of FIG. 12 uses the same 1-SN 900 of FIG. 9.However, the 1-SN 1165 is one of four (sub-networks 1155, 1165, 1175,1185) in a second part of a stage-2 scalable non-blocking switchingnetwork (2-SN) 1050 of FIG. 11A where the conductors 1151-1154,1161-1164, 1171-1174, 1181-1184 of the 2-SN are the M conductors 1060,1070, 1080, 1090 of the CLST4 circuits 1010, 1020, 1030, 1040,respectively of FIG. 10. Each of the CLST4 circuits 1010, 1020, 1030,1040 corresponds to the CLST4 circuit 100 of FIG. 1 along with the 1-SN900 of FIG. 9.

The TA1 circuit 1165 of FIG. 12 connects conductors 1201-1216selectively to conductors 1241-1256; 1241, 1245, 1249, 1253 that areconductors 1161 (N0[4-7]) of FIG. 11A which correspond to four of thesixteen M conductors 1060 (C0[4-7] of C0[0-15]) of CLST4 1010 of FIG.10. Similarly, conductors 1242, 1246, 1250, 1254 are conductors 1162 (N1[4-7]) of FIG. 11A which correspond to four of the sixteen M conductors1080 (C1[4-7] of C1[0-15]) of CLST4 1030 of FIG. 10. Conductors 1243,1247, 1251, 1255 are conductors 1163 (N2[4-7]) of FIG. 11A whichcorrespond to four of the sixteen M conductors 1070 (C2[4-7] ofC2[0-15]) of CLST4 1020 of FIG. 10. Conductors 1244, 1248, 1252, 1256are conductors 1164 (N3[4-7]) of FIG. 11A which correspond to four ofthe sixteen M conductors 1090 (C3[4-7] of C3[0-15]) of CLST4 1040 ofFIG. 10.

In a 1-SN implementation of the MTX 1050 circuit of FIG. 11A, M=64, k=4,and N=16, and in the 2-SN implementation, the number of sets of eachstage of intermediate conductors N0=4 and N1=4 where the product N0×N1is equal to N. The number of switches in the 2-SN 1050 of FIG. 10 usinga stronger connectivity SN discussed in FIG. 6 and FIG. 9 isM×N0+sum_(i=[1-N0])[(I0_(i)×N1)+sum_(j=[1-N1])(I1_(ij)×(I0_(i)/N1))]where I0_(i)=M/N0 for i=[1-N0], and I1_(ij)=I0_(i)/N1 for i=[1-N0],j=[1-N1] in network 1050 so I0_(i)=16, I1_(ij)=4 and the 2-SN of 1050has 768 switches. A 1-SN implementation would require 1280 switches, anda full cross bar switch would require 4096 switches. In the case whereeach I0_(i) conductors interface to (M−N0+1) instead of M of the Mconductors, and for each conductors interface to (I0_(i)-N1+1) insteadof I0_(i) of the I0_(i) conductors, the number of switches would be(M−N0+1)×N0+sum_(i=[1-N0])[(I0_(i)-N1+1)×N1)+sum_(j=[1-N1])(I1_(ij)×(I0_(i)/N1))].In the FIG. 10 case, we have N=N0×N1, I0_(i)=M/N0, I1_(ij)=M/N=k, thusthe number of switches in this case for the 2-SN is [M×(N0+N1+k)].

As discussed earlier, each of the N conductors of the k sets of Nconductors in the different SNs does not need to be of uniform size. ASN can be constructed with different sized N_(i)'s where the maximumsized N_(i) is used as the uniform sized new N and virtual conductorsand switches can be added to the smaller sized N_(i) making the N_(i)appear to be of size N. Since the interconnection specification will notrequire the smaller sized N_(i) to have more connections than N_(i)there is no change in the connectivity property of the SN. As anexample, in FIG. 1 instead of four sets of N conductors 101-104,105-108, 109-112, 113-116 as inputs for logic cells 10-40, respectively,logic cell 10 of FIG. 1 has only three inputs 101-103. In SN of FIG. 6with M conductors 601-612, switches in FIG. 6 and intermediateconductors 621-632 stay the same, with the exception that the threeswitches in sub-network 680 and conductor 104 are “virtual” and can betaken out of the SN in FIG. 6.

Multiple stages of scalable non-blocking switching networks can be builtusing the schemes described above, for example, the MTX 1050 of FIG. 10can be implemented as a stage-3 scalable non-blocking switching networkusing N0=2, N1=2 and N2=4 with first intermediate I0_(i) conductorsI0_(i)=M/N0, I1_(ij)=I0_(i)/N1 and I2_(ijk)=I1_(ij)/N2 for i=[1-N0],j=[1-N1] and k=[1-N2], where N0×N1×N2=N=16 which is the number of inputsfor each of the four CLST4 circuits 1010, 1020, 1030, 1040 of FIG. 10.Similarly, SN 1050 can be implemented as a stage-4 SN where N0=2, N1=2,N2=2 and N3=2 with four intermediate stages of conductors connecting theM conductors to the N conductors. The 2-SN implementation over the 1-SNimplementation in SN 1050 of FIG. 10 has a reduction in the number ofswitches by the difference between N×M=16M and (N0+N1)×M=(4+4)×M=8M; the3-SN and 4-SN where (N0+N1+N2)=(2+2+4)=8 and (N0+N1+N2+N3)=(2+2+2+2)=8,respectively, has no improvement over the 2-SN where (N0+N1)=(4+4)=8. Assuch, it may make sense only when the sum of Ni, the number of sets ofthe intermediate conductors for each stage, add up to be less than theprevious stage multi-stage SN. Thus, it can be seen that for N=64, a3-SN using N0=N1=N2=4 where (N0+N1+N2)=12 would be very effective inswitch reduction over a 2-SN using N0=N1=8 with (N0+N1)=16 and similarlyfor the 2-SN over 1-SN where N=64.

Thus we have described two levels of circuit hierarchy using scalablenon-blocking switching networks where sixty four M conductors fan in toconnect, through a 2-SN and then a 1-SN, to sixteen four-input logiccells. Sixteen of the sixty four M conductors are directly connected tothe sixteen outputs of each of the four CLST4 (125-128 of 100 in FIG. 1)circuits, providing unrestricted connections from any output to allsixteen logic cells. The first level of circuit hierarchy includes thecircuit CLST4 100 of FIG. 1 with MTX 200 implemented as the 1-SN 900 ofFIG. 9 where CLST4 100 has four four-input logic cells 10-40 and twoflip-flops 50, 60 as shown in FIG. 1. The next higher second level ofcircuit hierarchy is the CLST16 1000 circuits of FIG. 10 having fourCLST4 100 circuits with a 2-SN MTX16 1050 as shown in FIG. 10, where thenetwork 1050 implementation is illustrated in FIG. 11A, FIG. 11B andFIG. 12. In CLST16 1000, each of sixteen outputs 1065, 1075, 1085, 1095(connecting directly to conductors 1056) has unrestricted connectivityto every logic cell in the CLST16 1000 circuit and the other 48 Mconductors 1055 of FIG. 10 can be treated as the N conductors of theCLST16 1000 in building up the next level of circuit hierarchy. Thesixteen outputs 125-128 of CLST4 100 in FIG. 1 for each of the fourCLST4 circuits 1010, 1020, 1030, 1040 of FIG. 10 are directly wired tosixteen M conductors 1056, whose outputs can further connect, through aSN, to the next third level of circuit hierarchy using CLST16 1000circuits as building blocks and the forty-eight other M conductors arethe equivalent pins or input conductors for the CLST 1000 circuits toprovide continued high connectivity in the programmable logic circuit.

The CLST 1000 circuit of FIG. 10 is illustrated using a 2-SN cascadingfour 1-SNs with sixty four M conductors 1055, 1056 and sixteenfour-input logic cells organized in four groups 1010, 1020, 1030, 1040using a total of 1280 switches amongst the various SNs: SN 1050 of FIG.10 and SN 200 of FIG. 1 for each group 1010-1040 of FIG. 10. The CLST1000 circuit of FIG. 10 can have an alternative implementation using a1-SN with sixty four M conductors, k (e.g., 16) plurality of N (e.g., 4)conductors using the methods discussed in FIG. 9. The number of switchesis M×(N+k)=1280 using the analysis discussed herein. It turns out, inthis case, both the 1-SN implementation and the embodiment of FIG. 10has the same number of switches.

The decision in determining which implementation is more suitable willdepend on engineering considerations such as: whether a four-input MUXimplementation with more intermediate stages of conductors in the FIG.10 embodiment or sixteen-input MUX and less number of intermediatestages of conductors in the 1-SN implementation is more preferable usingSRAM technology, whether one style is more suitable in layoutimplementation, etc. It is important to note, based on the aboveanalysis, that it is preferable to have a reasonable sized base array oflogic cells connecting through a SN so the overhead, in total switchcount, in stitching up several base arrays of logic cells using anotherSN in the next level of circuit hierarchy does not exceed implementing alarger sized base array of logic cells. In most programmable logiccircuits, a base logic cell (of a logic cell array with a SN) usuallyhas either three inputs or four inputs, and it is reasonable to see,from the illustrated examples discussed above, the number of logiccells, k, in the base logic array should not be a small number, orrather, depending upon the size of N, k×N should be of reasonable size(e.g., the CLST4 100 circuit of FIG. 1) for a SN to be used efficientlyas the interconnect network.

Using numerous embodiments and illustrations, a detailed description inbuilding various scalable non-blocking switching networks is providedand used in various combinations to provide interconnect, both forinputs and outputs, for programmable logic circuits. Depending ontechnology and engineering considerations, variations in implementationof the scalable non-blocking switching networks may be used, including,but not exclusive of, the use of MUXs to reduce number of memorycontrols, switch reductions, etc.

What is claimed is:
 1. An integrated circuit, comprising a L-levelpermutable switching network (L-PSN); wherein the L-PSN comprises (L+2)levels of conductors and (L+1) sets of switches: wherein the (L+2)levels of conductors comprises: for each i=[1:L], (I[i]/D [i])>1,D[1]>1, L≧1, at least one j where D[j]>2 for a j selected from j=[1:L],the i-th level of conductors comprises I[i] number of conductorscomprising D[i] sets of conductors, wherein each of the D[i] sets ofconductors comprises (I[i]/D[i]) number of conductors; an 0-th level ofconductors of I[0] number of conductors, wherein(I[0]/Π_(i=[1:L])D[i])>1; an (L+1)-th level of conductors of I[L+1]number of conductors comprising D[L+1] sets of conductors, whereinD[L+1]>2, each of the D[L+1] sets of conductors comprises(I[L+1]/D[L+1]) number of conductors and(I[L+1]/D[L+1])=Π_(i=[1:L])D[i]; wherein each i-th set of the (L+1) setsof switches comprises at least (T[i]×D[i]) number of switches fori=[1:L+1] where T[i]=(I[i−1]−D[i]+1); wherein the Π_(i=[1:L])D[i] numberof conductors in each of the D[L+1] sets of conductors of the (L+1)-thlevel of conductors are physically connected to a corresponding numberof pins of a corresponding module selected from switching networks andlogic cells; wherein for each i=[1:L+1], at least T[i] number ofconductors of the I[i−1] number of conductors of the (i−1)-th level ofconductors selectively couple to (I[i]/D[i]) number of conductors ineach of the D[i] sets of conductors of the i-th level of conductorsthrough a respective plurality of at least T[i] number of switches ofthe i-th set of switches without requiring traversal of any otherconductors.
 2. The integrated circuit of claim 1, wherein for at leastone j selected from j=[1:L+1], each conductor of the (I[j]/D[j]) numberof conductors in each of the D[j] sets of conductors selectively couplesto at least (T[j]/(I[j]/D[j])) number of conductors of the at least T[j]number of conductors through a corresponding plurality of at least(T[j]/(I[j]/D[j])) number of switches without requiring traversal of anyother conductors.
 3. The integrated circuit of claim 1, wherein for atleast one j selected from j=[1:L+1], T[j]=I[j−1].
 4. The integratedcircuit of claim 3, wherein each conductor of the (I[j]/D[j]) number ofconductors in each of the D[j] sets of conductors selectively couples toat least (I[j−1]/I[j])×D[j] number of conductors of the I[j−1] number ofconductors through a corresponding plurality of at least(I[j−1]/I[j])×D[j] number of switches without requiring traversal of anyother conductors.
 5. A method to manufacture an integrated circuit,comprising: fabricating a L-level permutable switching network (L-PSN),wherein the L-PSN comprises (L+2) levels of conductors and (L+1) sets ofswitches: wherein the (L+2) levels of conductors comprises: for eachi=[1:L], (I[i]/D[i])>1, D[1]>1, L≧1, at least one j where D[j]>2 for a jselected from j=[1:L], the i-th level of conductors comprises I[i]number of conductors comprising D[i] sets of conductors, wherein each ofthe D[i] sets of conductors comprises (I[i]/D [i]) number of conductors;an 0-th level of conductors of I[0] number of conductors, wherein(I[0]/Π_(i=[1:L])D[i])>1; an (L+1)-th level of conductors of I[L+1]number of conductors comprising D[L+1] sets of conductors, whereinD[L+1]>2, each of the D[L+1] sets of conductors comprises(I[L+1]/D[L+1]) number of conductors and(I[L+1]/D[L+1])=Π_(i=[1:L])D[i]; wherein each i-th set of the (L+1) setsof switches comprises at least (T[i]×D[i]) number of switches fori=[1:L+1] where T[i]=(I[i−1]−D[i]+1); physically connecting theΠ_(i=[1:L])D[i] number of conductors in each of the D[L+1] sets ofconductors of the (L+1)-th level of conductors to a corresponding numberof pins of a corresponding module selected from switching networks andlogic cells; and for each i=[1:L+1], selectively coupling at least T[i]number of conductors of the I[i−1] number of conductors of the (i−1)-thlevel of conductors to (I[i]/D[i]) number of conductors in each of theD[i] sets of conductors of the i-th level of conductors through arespective plurality of at least T[i] number of switches of the i-th setof switches without requiring traversal of any other conductors.
 6. Themethod of claim 5, further comprising: for at least one j selected fromj=[1:L+1], selectively coupling each conductor of the (I[j]/D[j]) numberof conductors in each of the D[j] sets of conductors to at least(T[j]/(I[j]/D[j])) number of conductors of the at least T[j] number ofconductors through a corresponding plurality of at least(T[j]/(I[j]/D[j])) number of switches without requiring traversal of anyother conductors.
 7. The method of claim 5, wherein for at least one jselected from j=[1:L+1], T[j]=I[j−1].
 8. The method of claim 7, furthercomprising selectively coupling each conductor of the (I[j]/D[j]) numberof conductors in each of the D[j] sets of conductors to at least(I[j−1]/I[j])×D[j] number of conductors of the I[j−1] number ofconductors through a corresponding plurality of at least(I[j−1]/I[j])×D[j] number of switches without requiring traversal of anyother conductors.
 9. An article of manufacture comprising a machinereadable storage medium that stores data representing an integratedcircuit layout, comprising: a L-level permutable switching network(L-PSN); wherein the L-PSN comprises (L+2) levels of conductors and(L+1) sets of switches: wherein the (L+2) levels of conductorscomprises: for each i=[1:L], (I[i]/D [i])>1, D[1]>1, L≧1, at least one jwhere D[j]>2 for a j selected from j=[1:L], the i-th level of conductorscomprises I[i] number of conductors comprising D[i] sets of conductors,wherein each of the D[i] sets of conductors comprises (I[i]/D [i])number of conductors; an 0-th level of conductors of I[0] number ofconductors, wherein (I[0]/Π_(i=[1:L])D[i])>1; an (L+1)-th level ofconductors of I[L+1] number of conductors comprising D[L+1] sets ofconductors, wherein D[L+1]>2, each of the D[L+1] sets of conductorscomprises (I[L+1]/D[L+1]) number of conductors and(I[L+1]/D[L+1])=Π_(i=[1:L])D[i]; wherein each i-th set of the (L+1) setsof switches comprises at least (T[i]×D[i]) number of switches fori=[1:L+1] where T[i]=(I[i−1]−D[i]+1); wherein the Π_(i=[1:L])D[i] numberof conductors in each of the D[L+1] sets of conductors of the (L+1)-thlevel of conductors are physically connected to a corresponding numberof pins of a corresponding module selected from switching networks andlogic cells; wherein for each i=[1:L+1], at least T[i] number ofconductors of the I[i−1] number of conductors of the (i−1)-th level ofconductors selectively couple to (I[i]/D[i]) number of conductors ineach of the D[i] sets of conductors of the i-th level of conductorsthrough a respective plurality of at least T[i] number of switches ofthe i-th set of switches without requiring traversal of any otherconductors.
 10. The article of manufacture of claim 9, wherein for atleast one j selected from j=[1:L+1], each conductor of the (I[j]/D[j])number of conductors in each of the D[j] sets of conductors selectivelycouples to at least (T[j]/(I[j]/D[j])) number of conductors of the atleast T[j] number of conductors through a corresponding plurality of atleast (T[j]/(I[j]/D[j])) number of switches without requiring traversalof any other conductors.
 11. The article of manufacture of claim 9,wherein for at least one j selected from j=[1:L+1], T[j]=I[j−1].
 12. Thearticle of manufacture of claim 11, wherein each conductor of the(I[j]/D[j]) number of conductors in each of the D[j] sets of conductorsselectively couples to at least (I[j−1]/I[j])×D[j] number of conductorsof the I[j−1] number of conductors through a corresponding plurality ofat least (I[j−1]/I[j])×D[j] number of switches without requiringtraversal of any other conductors.